Integrated density of states for ergodic random Schrodinger operators on manifolds

被引：13

作者：

Peyerimhoff, N ^{[1
]}

Veselic, I ^{[1
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

GEOMETRIAE DEDICATA | 2002年 / 91卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

integrated density of states; random Schrodinger operators; Riemannian manifolds with compact quotient; amenable groups; ergodic theorem;

D O I：

10.1023/A:1016222913877

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Riemannian universal covering of a compact manifold M = X/Gamma and assume that Gamma is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrodinger operators on X.

引用

页码：117 / 135

页数：19

共 50 条

[41] Band edge behavior of the integrated density of states of random Jacobi matrices in dimension 1 [J].

Klopp, F .

JOURNAL OF STATISTICAL PHYSICS, 1998, 90 (3-4) :927-947

[42] Band Edge Behavior of the Integrated Density of States of Random Jacobi Matrices in Dimension 1 [J].

Frédéric Klopp .

Journal of Statistical Physics, 1998, 90 :927-947

[43] Lp-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity [J].

Michael J. Gruber ;

Daniel H. Lenz ;

Ivan Veselić .

Integral Equations and Operator Theory, 2011, 69 :217-232

[44] Poisson statistics for 1d Schrodinger operators with random decaying potentials [J].

Kotani, Shinichi ;

Nakano, Fumihiko .

ELECTRONIC JOURNAL OF PROBABILITY, 2017, 22

[45] ASYMPTOTIC BEHAVIOR OF THE INTEGRATED DENSITY OF STATES FOR RANDOM POINT FIELDS ASSOCIATED WITH CERTAIN FREDHOLM DETERMINANTS [J].

Ueki, Naomasa .

KYUSHU JOURNAL OF MATHEMATICS, 2019, 73 (01) :43-67

[46] The landscape law for the integrated density of states [J].

David, G. ;

Filoche, M. ;

Mayboroda, S. .

ADVANCES IN MATHEMATICS, 2021, 390

[47] Decorrelation Estimates for Random Discrete Schrodinger Operators in Dimension One and Applications to Spectral Statistics [J].

Shirley, Christopher .

JOURNAL OF STATISTICAL PHYSICS, 2015, 158 (06) :1298-1340

[48] Absolutely Continuous Spectrum for Random Schrodinger Operators on the Fibonacci and Similar Tree-strips [J].

Sadel, Christian .

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2014, 17 (3-4) :409-440

[49] Perturbations of continuum random Schrodinger operators with applications to Anderson orthogonality and the spectral shift function [J].

Dietlein, Adrian ;

Gebert, Martin ;

Mueller, Peter .

JOURNAL OF SPECTRAL THEORY, 2019, 9 (03) :921-965

[50] A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrodinger operators [J].

Gebert, Martin .

JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 277 (11)

← 1 2 3 4 5 →